Answer
increases by $2$ times
Work Step by Step
The variation model described by the problem is $
V=khr^2
,$ where $V$ is the volume, $h$ is the height, and $r$ is the radius.
If $h=2$ and $r=1,$ then
\begin{array}{l}\require{cancel}
V_1=k(2)(1)^2
\\
V_1=k(2)(1)
\\
V_1=2k
.\end{array}
If $h=1$ (height is halved) and $r=2$ (radius is doubled), then
\begin{array}{l}\require{cancel}
V_2=k(1)(2)^2
\\
V_2=k(1)(4)
\\
V_2=4k
.\end{array}
Comparing $V_1$ and $V_2$, when $h$ is halved and $r$ is doubled, the volume increases by $2$ times.
